NATURAL CONVECTION OF AIR IN A SQUARE CAVITY D ... - ICHMT

NATURAL CONVECTION OF AIR IN A SQUARE CAVITYD.Akrour * , R.Bennacer ** and D.Kalahe * .*Laboratoire de Mécanique des Fluides, Faculté de PhysiqueBP 32 El-Alia, Bab-Ezzouar16111, Alger, AlgeriaFax:0021321247344 e-mail: dalila_akrour@yahoo.com**Université de Cergy Pontoise, FranceIn the present numerical study, three-dimensional steady flow analyses has been made on naturalconvection in a differentially heated cubical enclosure.The detailed structures of the three-dimensional fields were scrutinised by using high resolutioncomputational results over the range of Rayleigh numbers studied 10 3 ≤ Ra ≤ 10 6 .In this work 42*42*42 mesh frame is used in the x, y and z directions for 10 3 ≤ Ra ≤ 5.10 4 and52*52*52 for Ra ≥ 10 5 ( figure –1-)Fig.1. Grid distribution of computational domainExamination of the perspective three dimensional fields revealed that the variations in the z-direction were evident particularly near the end wall. As the Rayleigh number increases, theconvective activities intensify and significant z-variation tend to be confined into narrower areasclose to the end walls, this is a result of boundary layer development .

The analysis is conducted by observing variation of the velocity vectors, pathlines and isothermsfor different Rayleigh numbers. The details of the three dimensional flow and isotherms aredescribed in order to investigate the effects of three dimensionalities on the fluid flow and thermalcharacteristics in enclosure.The variation of Nusselt numbers on the hot and cold walls are also presented to show the overallheat transfer characteristics inside the enclosure. The three-dimensional data demonstratereasonable agreement with the experimental measurement.Utilizing the above numerical results, heat transfer correlation over 10 3 ≤ Ra ≤ 10 6 for the threedimensional enclosure are proposed as : Nu=0.1291.Ra 0.304 ( figure-2-)7,38906Nu=0.1291*Ra 0.304Nusselt Number at cold wall2,7182818103,08393 59874,14172 442413,39201RaFig-2-: The overall Nusselt number at the colder wallThe predicted overall Nusselt number shows considerable discrepancies from the correspondingtwo dimensional solutions.Keywords : Numerical simulation, 3-D natural convection , multigrid method.REFERENCES1. I.Sezai, A.A.Mohamad, Natural convection from a discrete heat source on the bottom ofhorizontal enclosure, I.J.H.M.T, 43, p.2257-2266 (2000).2. J.Pallares, F.X.Grau, Franese Giralt, Flow transitions in laminar Rayleigh-Benardconvection in a cubical cavity at moderate Rayleigh numbers, I.J.H.M.T,4 2 ,p.753-769 (1999).